The problem in the image asks you to:

• Solve for $y$,
• Sketch the graph,
• Apply the given domain, $x \in \{-5, -1.5, 6, 10\}$.

Step 1: Solve for $y$

The equation is already given as $y = 8$. This is a horizontal line where the value of $y$ remains constant at 8 for any value of $x$.

Step 2: Apply the Domain

The domain provided is a set of specific $x$-values: $x = -5, -1.5, 6, 10$. For each of these values of $x$, the corresponding $y$-value is always 8.

So the points you will plot are:

• $(-5, 8)$
• $(-1.5, 8)$
• $(6, 8)$
• $(10, 8)$

Step 3: Sketch the Graph

Since the equation is $y = 8$, plot a horizontal line passing through $y = 8$. Then, mark the points where $x$ takes the values $-5, -1.5, 6, 10$ and $y$ is always 8.

Would you like more details or have any questions about these steps?

Here are 5 related questions to expand your understanding:

1. What is the significance of a horizontal line on a graph?
2. How do you determine the range when given a horizontal line equation?
3. What happens to the graph if the value of $y$ changes?
4. How would the graph change if you had a vertical line instead?
5. How do you calculate the slope of a horizontal line?

Tip: A horizontal line has a slope of 0 since the value of $y$ remains constant, no matter the value of $x$.